A pyramidal carbocation is a type of carbocation with a specific configuration. This ion exists as a third class, besides the classical and non-classical ions. In these ions, a single carbon atom hovers over a four- or five-sided polygon, in effect forming a pyramid. The four-sided pyramidal ion will carry a charge of 1+, and the five-sided pyramid will carry 2+. In the images (at upper right), the black spot on the vertical line represents the hovering carbon atom. The apparent coordination number of five, or even six, associated with the carbon atom at the top of the pyramid is a rarity as compared to the usual maximum of four.
History Studying these cations was sparked, at the time, by amazing results in computational chemistry. While calculating the optimal geometry of the mono-cation which arises from the extraction of chloride from 3-chlorotricyclo[2.1.0.02,5]pentane, the three bridges were expected to orient in space with angles of roughly 120°. The calculations however showed the four-sided pyramid to be the most stable configuration. At the top of this pyramid, there resides a carbon atom, still connected to a hydrogen. The original expected structure turned out to be not even close to an energy minimum: it represented a maximum.
Figure 1: Several possibilities for (CH)5 cation.
1a starting situation in the calculations: the chloride ion just left. 1b the expected structure. Charge has been delocalized over three carbon atoms 1c representation of the pyramidal ion. Depending on the method used, the ion 1c in figure 1 is an absolute or just a relative minimum.
Theoretical background A complete theoretical discussion will use all orbitals of all contributing atoms. A first approximation might use a LCAO of the molecular orbitals in the polygon forming the base of the pyramid and the orbitals on the apical atom, as the carbon atom at the top of the pyramid. This approximation will provide insight into the intrinsic stability of the structures.
Apical carbon atom The apical carbon atom is connected to only one other substituent, so an sp-hybridisation is to be expected. The substituent will be oriented upward. Towards the basic polygon, three orbitals are available:
The second sp-orbital. This orbital is relatively low in energy due to the contribution of the s-orbital. With respect to the nodal planes in the remaining p-orbitals the symmetry of this orbital can be written as SxSy, symmetric with respect to both planes. The orbital has a rather low energy, in terms of the Hückel method its value is not easy to estimate, although it will be lower than α, since the orbital will have considerable s-character. Two p-orbitals. These orbitals have a higher energy content then the sp-orbital. In terms of the Huckel method, the energy will be α. In symmetry terms, these orbitals are orthogonal, described as AxSy and SxAy
Base of the pyramid
The approximation for the base of the pyramid is a closed ring of carbon atoms, all of them sp2 hybridised. The exact results depend on the ring size; overall conclusions can be formulated as:
The lowest molecular orbital has, watched from the apex of the pyramid, no nodal planes. Symmetry will be SxSy. In the Hückel method, its energy is (α - 2β) The next level of energy is occupied by two degenerated orbitals. In symmetry terms, they are written as SxAy and AxSy. The energy depends on the size of the ring:
Depending on the size of the base, there will be other MOs, but they are irrelevant to the present discussion.
Interaction between apex and base To obtain bonding interactions between atoms or parts of molecules, two conditions should be met:
The orbitals to combine should have the same symmetry. A smaller difference in energy between the combining orbitals will produce a greater stabilizing effect. The orbitals at the apical carbon and the basic polygon are able to combine with respect to their symmetries. The result will be a more stable configuration for the pyramids. In figure 2, the symmetry aspects are depicted.
The apical sp orbital combines with the lowest MO of the basic ring to a low bonding and a high anti-bonding orbital. The two apical p orbitals combine with the second lowest energy levels in the basic ring. Two bonding and two anti-bonding orbitals result. Figure 3 is a graphical representation of the results. Filling the atomic and molecular orbitals in pyramidal structures of different base size leads to the next table. Only bonding orbitals are accounted for.
In the case of the three-sided pyramid, clearly no ion results; a known neutral species arises: tetrahedrane. To this molecule this way of description is an alternative quantum mechanical description. The other pyramidal structures will be charged in relation with their base size.
Examples
Monocation Figure 4: A number of derivatives of tricyclo[2,1,0,02,4]pentane (TCP) leading to the same pyramidal cation. The carbon atom carrying the leaving group becomes basic, while carbon at the anti position becomes apical.The group "R" is either 1H or 2H (D):
In 1972 Masamune describes the results of dissolving a number of precursors to 4d (figure 4) at - 70°C. in superacid (a mixture of SO2ClF and FSO3H). Based on both the 13C as well as the 1H-NMR-spectrum the evidence is clear: in each case the same intermediary is formed. Also, when the super acidic medium is destroyed, with either methanol or benzoic acid, the same product is formed. (see: Reaction... below).
Assignment in the hydrogen spectrum is partly on intensity (hydrogens at the basic ring) partly on the common experience hydrogen's at the outer side of a circular conjugated system have signals at higher ppm relative to TMS, while those positioned over the ring will have lower, even negative, signals relative to TMS. Assignment in 13C-NMR follow the same considerations as for 1H. Though in carbon NMR intensity is a bad guide to the number of atoms, in the basic ring the unsubstituted carbons are similar enough to use intensity as indication for their number. A powerful tool too is the multiplicity of the carbon signal due to coupling with the to carbon bonded hydrogens. Masamune himself does not state anything about the nature of the intermediate ion. Nevertheless, based on rules formulated by Olah, he is able to rule out localized cations (like 1-butyl) or delocalized ones (like allyl). For those ions signals around 200 ppm are expected.
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